The difference between smoking and grilling is when you are smoking you are cooking at a relatively low temperature for a longer amount of time as to obtain maximum smoke absorption. When you are grilling, you are cooking at a higher heat in order to obtain a nice sear on your food.

Sometimes I will do both on the same cut of meat. For instance, when I am cooking steaks on the grill. I will smoke some steaks for
couple of hours until the reach 120 degrees, and then I will crank up the heat and sear them on both sides until they reach 135 degrees for a nice medium rare.